scholarly journals On Maximum-Sized Golden-Mean Matroids

2021 ◽  
Author(s):  
◽  
Michael Welsh
Keyword(s):  
High Rank ◽  
Golden Mean ◽  
Root Of Unity ◽  
Simple Matroid

<p>A rank-r simple matroid is maximum-sized in a class if it has the largest number of elements out of all simple rank-r matroids in that class. Maximum-sized matroids have been classified for various classes of matroids: regular (Heller, 1957); dyadic (Kung and Oxley, 1988-90); k-regular (Semple, 1998); near-regular and sixth-root-of-unity (Oxley, Vertigan, and Whittle, 1998). Golden-mean matroids are matroids that are representable over the golden-mean partial field. Equivalently, a golden-mean matroid is a matroid that is representable over GF(4) and GF(5). Archer conjectured that there are three families of maximum-sized golden-mean matroids. This means that a proof of Archer’s conjecture is likely to be significantly more complex than the proofs of existing maximum-sized characterisations, as they all have only one family. In this thesis, we consider the four following subclasses of golden-mean matroids: those that are lifts of regular matroids, those that are lifts of nearregular matroids, those that are golden-mean-graphic, and those that have a spanning clique. We close each of these classes under minors, and prove that Archer’s conjecture holds in each of them. It is anticipated that the last of our theorems will lead to a proof of Archer’s conjecture for golden-mean matroids of sufficiently high rank.</p>

scholarly journals On Maximum-Sized Golden-Mean Matroids

2021 ◽  
Author(s):  
◽  
Michael Welsh
Keyword(s):  
High Rank ◽  
Golden Mean ◽  
Root Of Unity ◽  
Simple Matroid

<p>A rank-r simple matroid is maximum-sized in a class if it has the largest number of elements out of all simple rank-r matroids in that class. Maximum-sized matroids have been classified for various classes of matroids: regular (Heller, 1957); dyadic (Kung and Oxley, 1988-90); k-regular (Semple, 1998); near-regular and sixth-root-of-unity (Oxley, Vertigan, and Whittle, 1998). Golden-mean matroids are matroids that are representable over the golden-mean partial field. Equivalently, a golden-mean matroid is a matroid that is representable over GF(4) and GF(5). Archer conjectured that there are three families of maximum-sized golden-mean matroids. This means that a proof of Archer’s conjecture is likely to be significantly more complex than the proofs of existing maximum-sized characterisations, as they all have only one family. In this thesis, we consider the four following subclasses of golden-mean matroids: those that are lifts of regular matroids, those that are lifts of nearregular matroids, those that are golden-mean-graphic, and those that have a spanning clique. We close each of these classes under minors, and prove that Archer’s conjecture holds in each of them. It is anticipated that the last of our theorems will lead to a proof of Archer’s conjecture for golden-mean matroids of sufficiently high rank.</p>

Which human qualities can economic liberalism be based on?

2015 ◽  
pp. 5-24 ◽  
Author(s):  
V. Avtonomov
Keyword(s):  
Economic Policy ◽  
Human Values ◽  
High Rank ◽  
Economic Liberalism ◽  
Von Mises ◽  
Liberal Policy

The article asks which human qualities can serve as the base for a liberal economic policy. The author is looking for an answer to this question in the classical works of economic liberalism - in the books by F. Bastiat, L. von Mises, F. von Hayek, W. Eucken, and M. Friedman. The two main qualities can be summarized as follows: the relatively high rank of freedom among human values and rational utilitarian calculus. It is assumed that in those countries where the both human prerequisites are present the liberal policy (for instance, liberal reforms) can be self-supportive and may have good results. On the contrary, if the first prerequisite is missing and a liberal policy can be based only on rational calculus, the “paternalistic” liberalism prevails and chances for success are much smaller.

scholarly journals Influence of depressurization rate on gas production capacity of high-rank coal in the south of Qinshui Basin, China

2019 ◽  
Vol 46 (3) ◽  
pp. 642-650 ◽  
Author(s):  
Xuefeng SU ◽  
Yan LIU ◽  
Zhouqi CUI ◽  
Jianguo ZHANG ◽  
Li YU ◽  
...  
Keyword(s):  
Production Capacity ◽  
Gas Production ◽  
High Rank ◽  
The South ◽  
Qinshui Basin

scholarly journals Ramification Theory for Extensions of Degree p. II

1972 ◽  
Vol 46 ◽  
pp. 97-109
Author(s):  
Susan Williamson
Keyword(s):  
Valuation Ring ◽  
Quotient Field ◽  
Root Of Unity ◽  
Ramification Index ◽  
Ramification Theory ◽  
Rank One ◽  
The Absolute

Let k denote the quotient field of a complete discrete rank one valuation ring R of unequal characteristic and let p denote the characteristic of R̅; assume that R contains a primitive pth root of unity, so that the absolute ramification index e of R is a multiple of p — 1, and each Gallois extension K ⊃ k of degree p may be obtained by the adjunction of a pth root.

scholarly journals Redox homeostasis: The Golden Mean of healthy living

Redox Biology ◽  
2016 ◽  
Vol 8 ◽  
pp. 205-215 ◽  
Author(s):  
Fulvio Ursini ◽  
Matilde Maiorino ◽  
Henry Jay Forman
Keyword(s):  
Redox Homeostasis ◽  
Healthy Living ◽  
Golden Mean

scholarly journals p-adic confluence of q-difference equations

2008 ◽  
Vol 144 (4) ◽  
pp. 867-919 ◽  
Author(s):  
Andrea Pulita
Keyword(s):  
Differential Equation ◽  
Difference Equation ◽  
Differential Equations ◽  
Difference Equations ◽  
Root Of Unity

AbstractWe develop the theory of p-adic confluence of q-difference equations. The main result is the fact that, in the p-adic framework, a function is a (Taylor) solution of a differential equation if and only if it is a solution of a q-difference equation. This fact implies an equivalence, called confluence, between the category of differential equations and those of q-difference equations. We develop this theory by introducing a category of sheaves on the disk D−(1,1), for which the stalk at 1 is a differential equation, the stalk at q isa q-difference equation if q is not a root of unity, and the stalk at a root of unity ξ is a mixed object, formed by a differential equation and an action of σξ.

Knowledge Spaces with Arbitrarily High Rank

1998 ◽  
Vol 22 (2) ◽  
pp. 260-273 ◽  
Author(s):  
Aviad Heifetz ◽  
Dov Samet
Keyword(s):  
High Rank ◽  
Knowledge Spaces
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